Over 57 games, Wood was 2-5 with a 3.53 ERA and an International League-leading 29 saves. Over his 58 2/3 innings, he walked 25 and struck out 70 while allowing 52 hits.
Wood also led that league with 46 games finished and a 10.74 strikeouts-per-nine-innings ratio.
In 115 big league appearances from 2010-14 with the Royals and Indians, Wood has a 4.39 ERA. He worked a career-high 55 games for Kansas City in 2011 and posted a 3.75 ERA.
A torn ulnar collateral ligament in his right elbow during the 2012 season required Tommy John surgery, and he was claimed off of waivers by Cleveland following that season.
Cincinnati has been looking to overhaul its bullpen after a rough season of performances, especially in the middle innings, which has several roles wide open for competition heading toward Spring Training. The bullpen's best pitcher, Aroldis Chapman, is available for trade.
With Wood's signing, combined with the addition of three prospects on Thursday, the Reds have 38 players on their 40-man roster.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, follow him on Twitter @m_sheldon and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.